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1. In a study of faculty salaries in a small college in the Midwest, a linear re

ID: 3051461 • Letter: 1

Question

1. In a study of faculty salaries in a small college in the Midwest, a linear regression model was fit Y = Salary and 11 = Sex. giving the estimated regression function Y = 24607-3340n where zi = 1 if the faculty member was finale and 0 if male. The response Salary is measured in dollars (the data are from the 1970s). (a) Give a sentence that describes the meaning of the two estimated coeficients. b) An alternative model to the data set has an additional term, 2-Years, e, the number of years employed at this college. The estimated regression function is =1065 + 20111 + 750r2 The important difference bet ween these two estimated regression functions is that the coefficient for i has changed signs. Provide an explanation as to how this could happen

Explanation / Answer

a) The coefficient of 24697 is the intercept which shows the maximum salary and if we put the value of x1 as 0, that is male then it bacomes the salary of the male faculty member.

    For female the -3340 coefficient decreases the intercept value to get the value of salary. So this coefficient tells that the females get less salary compared to male by 3340 units since it has negative sign.

b) Now in the second equation the intercept value is reduced and the coefficient of x1 is positive which indicates the famles get more salary than male. But here a new variable is added which is years. So it shows that males actually work for more years than females and so females have less salary as compared to males from the first equation. So this takes care of the number of years employed. So actually females are getting paid higher but males work for more years and so they get higher salary compared to less experienced females from the first equation.